Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x?

The possible values of x are 90°, 30° and 150°.

Step-by-step explanation:

Given that,

sin(2x) = cos(x) where 0° ≤ x < 180°

We know that, sin(2x) = 2 sinx cosx

2 sinx cosx = cosx

Subtract cosx on both sides

2 sinx cosx - cosx = 0

cosx (2sinx-1)=0

It means, cosx = 0 and (2sin x -1 ) = 0

cos x = cos0           and        sinx = 1/2

x = 90°                     and        x = 30°, 150°

Hence, the possible values of x are 90°, 30° and 150°.